In this work, the Rössler system is used as a model for chrono therapy. We applied a periodic perturbation to the y variable to take the Rössler system from a chaotic behavior to a simple periodic one, varying the period and amplitude of forcing. Two types of chaos were considered, spiral and funnel chaos. As a result, the periodical windows reduced their areas as the funnel chaos character increased in the system. Funnel chaos, in this chrono therapy model, could be considered as a later state of a dynamical disease, more irregular and difficult to suppress.
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http://dx.doi.org/10.3934/mbe.2007.4.177 | DOI Listing |
Chaos
August 2022
CNRS-IRD-CONICET-UBA, Institut Franco-Argentin d'Études sur le Climat et ses Impacts (IRL 3351 IFAECI), C1428EGA CABA, Argentina.
The theory of homologies introduces cell complexes to provide an algebraic description of spaces up to topological equivalence. Attractors in state space can be studied using Branched Manifold Analysis through Homologies: this strategy constructs a cell complex from a cloud of points in state space and uses homology groups to characterize its topology. The approach, however, does not consider the action of the flow on the cell complex.
View Article and Find Full Text PDFEntropy (Basel)
September 2018
Department of Radio Electronics, FEEC, Brno University of Technology, 601 90 Brno, Czech Republic.
This paper brings analysis of the multiple-valued memory system (MVMS) composed by a pair of the resonant tunneling diodes (RTD). Ampere-voltage characteristic (AVC) of both diodes is approximated in operational voltage range as common in practice: by polynomial scalar function. Mathematical model of MVMS represents autonomous deterministic dynamical system with three degrees of freedom and smooth vector field.
View Article and Find Full Text PDFChaos
July 2018
Cardiology Department, Canberra Hospital, Yamba Drive, Garran, Australian Capital Territory 2605, Australia.
Previous studies have suggested benefits of applying fractal analysis to intervals between R waves in electrocardiography as an additional prognostic marker. The aim of this study was to investigate whether fractal analysis can provide an independent predictor of cardiac mortality or all-cause mortality. Prognostic cohort studies reporting fractal heart rate variability results from 24-h Holter monitor recordings were selected for comparison.
View Article and Find Full Text PDFChaos
July 2017
Department of Physics, National Taiwan University, Taipei 10617, Taiwan.
We investigate the behavior of a typical trajectory in a funnel type Rössler attractor. Using a suitable averaging method, we propose to describe the originally more difficult time-continuous chaotic behavior of the system using an approximate four-parameter surrogate iteration scheme. This approach has the merits of helping one see more easily how the height of the peaks and the peak-to-peak durations vary as one tunes the system parameters.
View Article and Find Full Text PDFChaos
December 2007
Department of Physics and Applied Math, Universidad de Navarra, Irunlarrea s/n, E-31080 Pamplona, Spain.
We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled.
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